1. Field of the Invention
The present invention relates to a method of generating a threshold matrix for producing a color separation, a method of reproducing a color image, an apparatus for producing a color separation, and a threshold matrix, for producing each of color separations, the threshold matrix converting a continuous-tone image subjected to color separation into a dot pattern for each of the color separations, a color image being reproduced by overlaying the dot patterns, the dot pattern being a binary image in which no screen ruling or screen angle is defined. More particularly, the present invention relates to a method of generating a threshold matrix for producing a color separation, a method of reproducing a color image, an apparatus for producing a color separation, and a threshold matrix, which are preferably applicable to a printing-related apparatus (output system) such as a filmsetter, a CTP (Computer To Plate) apparatus, a CTC (Computer To Cylinder) apparatus, a DDCP (Direct Digital Color Proof) system, etc., an ink jet printer, or an electrophotographic printer, for example.
A dot pattern representative of a binary image in which no screen ruling or screen angle is defined is called a pattern of an FM screen or a stochastic screen.
2. Description of the Related Art
Heretofore, so-called AM (Amplitude Modulation) screens characterized by screen ruling, screen angle, and dot shape, and FM (Frequency Modulation) screens have been used in the art of printing.
A process of generating a threshold matrix for FM screens is disclosed in Japanese Laid-Open Patent Publication No. 8-265566.
According to the disclosed process, an array of elements of a threshold matrix, i.e., an array of thresholds, is generated in an ascending order or a descending order by determining threshold positions such that the position of an already determined threshold is spaced the greatest distance from the position of a threshold to be newly determined. The dot pattern of a binary image that is generated using the threshold matrix thus produced has dots which are not localized. Even when a dot pattern is generated using a plurality of such threshold matrixes that are juxtaposed, the dot pattern does not suffer a periodic pattern produced by the repetition of threshold matrixes.
A plurality of patent documents given below are relevant to the generation of a threshold matrix.
Japanese Patent No. 3400316 discloses a method of correcting halftone image data by extracting a pixel having a weakest low-frequency component of a certain dot pattern, from white pixels (unblackened pixels), and a pixel having a strongest low-frequency component of the dot pattern, from blackened pixels, and switching around the extracted white and blackened pixels. Thus, the dot pattern is intended to be smoothed or leveled.
Japanese Laid-Open Patent Publication No. 2001-292317 reveals a process of determining threshold positions in a threshold matrix such that a next blackened pixel is assigned to a position having a weakest low-frequency component of the threshold matrix.
Japanese Laid-Open Patent Publication No. 2002-368995 shows a process of determining threshold positions in a threshold matrix such that when an array of thresholds in the threshold matrix has been determined up to a certain gradation and a threshold position for a next gradation is to be determined, blackened pixels are assigned to positions for not strengthening a low-frequency component.
Japanese Laid-Open Patent Publication No. 2002-369005 discloses a process of generating a threshold matrix according to the process shown in Japanese Patent No. 3400316, Japanese Laid-Open Patent Publication No. 2001-292317 or Japanese Laid-Open Patent Publication No. 2002-368995, based on an ideal dot pattern at a certain gradation which is given.
When an FM screen is used for offset printing, it causes shortcomings in that the quality of printed images suffers some graininess (grainness). FM screens also cause disadvantages in that a dot gain tends to become large and images are reproduced unstably when images are printed, or when films are output in an intermediate printing process, or when a printing plate is output by a CTP apparatus.
According to the conventional FM screening process, when a dot size is determined to be the size of a dot made up of one pixel or a dot made up of four pixels according to a 1 (1×1)-pixel FM screen or a 4 (2×2)-pixel FM screen, an array of thresholds of a threshold matrix is determined by an algorithm for generating FM screens, thus determining an output quality, and only the dot size serves as a parameter for determining the quality of FM screens. For example, if a dot size is determined to be a 3×3-pixel FM screen dot size with respect to an output system which is incapable of stably reproducing 2×2-pixel FM screen dots for highlight areas, then the resolution (referred to as pattern frequency or pattern resolution) for intermediate tones is lowered, resulting in a reduction in the quality of images.
FIG. 27 of the accompanying drawings shows a conventional dot pattern 1 in a highlight area HL where the dot percentage of a 2×2-pixel FM screen is 5%, a conventional dot pattern 2 in an intermediate tone area where the dot percentage of the 2×2-pixel FM screen is 50%, a conventional dot pattern 3 in a highlight area HL where the dot percentage of a 3×3-pixel FM screen is 5%, and a conventional dot pattern 4 in an intermediate tone area where the dot percentage of the 3×3-pixel FM screen is 50%.
FIG. 28 of the accompanying drawings shows a power spectrum generated when the dot pattern 2 of the 2×2-pixel FM screened shown in FIG. 27 is FFTed (Fast-Fourier-Transformed), and FIG. 29 of the accompanying drawings shows a power spectrum generated when the dot pattern 4 of the 3×3-pixel FM screen shown in FIG. 27 is FFTed.
In FIG. 27, at the dot percentage of 50% in the intermediate tone area, the dot pattern 2 of the 2×2-pixel FM screen suffers less graininess than the dot pattern 4 of the 3×3-pixel FM screen, but has the dot percentage less reproducible in the printed image. On the other hand, at the dot percentage of 50% in the intermediate tone area, a peak value of the dot pattern 4 of the 3×3-pixel FM screen has a pattern frequency 6 of about 13 c/mm which is lower than the pattern frequency 5 of about 20 c/mm of the dot pattern 2 of the 2×2-pixel FM screen. The pattern frequencies 5, 6 which are of peak values are also called a peak spatial frequency fpeak.
The output resolution of an output system such as an imagesetter, a CTP (Computer To Plate) apparatus, etc. (the output resolution of an output system will hereinafter be referred to as output resolution R) is set to 2540 pixels/inch=100 pixels/mm or 2400 pixels/inch=94.488 pixels/mm, for example. With those settings, the dot size of the 1×1 pixel FM screen is 10 μm×10 μm (or 10.6 μm×10.6 μm), and the dot size of the 2×2 pixel FM screen is 20 μm×20 μm (or 21.2 μm×21.2 μm).
In this description, the output resolution R is different from the pattern frequencies 5, 6 (fpeak) of the dot patterns 2, 4 shown in FIGS. 27, 28.
Technical solutions for the above problems are suggested in Japanese Laid-Open Patent Publication No. 2005-252881.
Japanese Laid-Open Patent Publication No. 2005-252881, however, aims to reduce graininess in an image when a single color separation is used. Then, it has been found that the graininess may be recognized when a color image is reproduced by overlaying a plurality of color separations, even if the graininess is not recognized in an image as a single separation.
Specifically, this problem will be described below, referring to a color image shown in FIG. 30C obtained by overlaying (superimposing) two major color separations of a C-separation (Cyan) shown in FIG. 30A and an M-separation (Magenta) shown in FIG. 30B.
FIG. 30A illustrates a dot pattern 302 for the C-separation in the space domain. FIG. 30B illustrates a dot pattern 304 for the M-separation in the space domain. FIG. 30C illustrates a dot pattern 306 of a color image obtained by overlaying the dot patterns 302, 304 for the C-separation and the M-separation. In the overlaid dot pattern 306 of a color image, a low-frequency component, i.e., the graininess is recognized.
In this explanation, a dot percentage of the dot patterns 302, 304 is 50%. It is also possible to confirm whether the graininess is recognized when dot patterns having arbitrary dot percentages are overlaid, e.g., a dot pattern with a dot percentage of 40% and a dot pattern with a dot percentage of 55%.
FIG. 30D illustrates frequency-domain data 308 obtained by the Fourier Transform of the dot pattern 302. FIG. 30E illustrates frequency-domain data 310 obtained by the Fourier Transform of the dot pattern 304. FIG. 30F illustrates frequency-domain data 312 obtained by the Fourier Transform of the dot pattern 306. The deep black portion in the frequency-domain data 308, 310, 312 corresponds to the portion where the frequency component is strong.
The frequency-domain data 312 shown in FIG. 30F can be obtained through the convolution operation of the frequency-domain data 308 and the frequency-domain data 310.
Each of the frequency-domain data 308, 310, 312 has each of main frequency components 308p, 310p, 312p, and a minute component. Each of the main frequency components 308p, 310p, 312p has a ring shaped distribution with a constant range ±Δ and a radius (pattern frequency or peak frequency) r. The minute component spreads over the entire frequency domain appearing a light gray color, but is not visually recognized as the graininess of a low frequency component. However, in the overlaid frequency-domain data 312, it is recognized that a low frequency component 314 including the frequency component of zero is present. It has been found that the low frequency component 314 causes a low frequency component in the dot pattern 306 of a color image, i.e., the graininess in the image.
In the explanation below, when illustrating that the dot pattern in the space-domain is converted into the components in the frequency-domain, only main frequency components forming some shape such as a ring and partial rings, and low frequency components causing the graininess will be illustrated in the figures. Other minute components unrelated to the graininess will not be illustrated for easy understanding of the figures.